Related papers: A Breakthrough in Sphere Packing: The Search for M…
We analyze Sz\"oll\H{o}si's recent construction of a conjecturally optimal five-dimensional kissing configuration and produce a new such configuration, the fourth to be discovered. We construct five-dimensional sphere packings from these…
This article (which appeared with illustrations) was the astrophysics/cosmology contribution to the historical series ``Pathways of Discovery'' which appeared in ``Science'' during last year.
The IceCube, Pierre Auger and Telescope Array Collaborations have recently reported results on neutral particles (neutrons, photons and neutrinos) which complement the measurements on charged primary cosmic rays at ultra-high energy. The…
We prove a lower bound on the entropy of sphere packings of $\mathbb R^d$ of density $\Theta(d \cdot 2^{-d})$. The entropy measures how plentiful such packings are, and our result is significantly stronger than the trivial lower bound that…
Wormholes are extremely attractive objects for research, and although many mathematical and physical properties of these objects have been discovered and studied in the recent decades, there remain many unsolved problems and opportunities…
In 1975, two papers were published that together sparked major new directions, conceptual, mathematical and practically applicable, in several previously disparate fields of science. In this short review, we expose key aspects of their…
Despite the undeniable success of the Standard Model of particle physics (SM) there are some phenomena (neutrino oscillations, baryon asymmetry of the Universe, dark matter, etc.) that SM cannot explain. These phenomena indicate that the SM…
We describe here experiments on the mechanics of hydrogel particle packings from the Behringer lab, performed between 2012 and 2015. These experiments quantify the evolution of all contact forces inside soft particle packings exposed to…
We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bi-cromatic packing known up to now.
Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static…
A very brief overview is presented on some of the current most active areas of research in formal aspects of High Energy Physics and Cosmology. Including the recent breakthrough on the black hole information paradox, developments on…
This article is a brief review of the research by Dr. C. de Jager and co-workers over the past twenty years into the physics of hypergiant atmospheres. Various important results on the microturbulence, mass-loss, circumstellar environment,…
The purpose of this paper is point out connections between scattering theory, double operator integrals, Kreins spectral shift function, integration theory, bimeasures, Feynman path integrals, harmonic and functional analysis and many other…
In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only led to interesting mathematics, but has also found…
Many new results on open and hidden charm spectroscopy have been obtained recently. We present a short review of the experimental findings in the meson sector, of the theoretical interpretations and of the open problems, with a discussion…
We prove sphere packing density bounds in hyperbolic space (and more generally irreducible symmetric spaces of noncompact type), which were conjectured by Cohn and Zhao and generalize Euclidean bounds by Cohn and Elkies. We work within the…
We describe a program to prove the Kepler conjecture on sphere packings. We then carry out the first step of this program. Each packing determines a decomposition of space into Delaunay simplices, which are grouped together into finite…
Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made…
This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two…
Availability of reliable atomic and molecular opacity tables is essential in a wide variety of astronomical modeling: the solar and stellar interiors, stellar and planetary atmospheres, stellar evolution, pulsating stars, and protoplanetary…